A Global System for Mobile Communications (GSM) system, which is a sort of mobile communication systems, is a personal portable communication system (or technology) widely used over the world, and is a communication system based on Time Division Multiple Access (TDMA).
FIG. 1 illustrates a baseband equivalent system model in a mobile communication system.
Referring to FIG. 1, in a GSM system, the baseband equivalent system model may include a digital transmitter (or a transmitting apparatus) 100, a wireless channel 110, and a receiver (or a receiving apparatus) 120.
The transmitter 100 generates and transmits a signal according to an Enhanced Data GSM Environment (EDGE) physical channel specification of GSM. In the transmitter 100, a random bit signal in which “0” and “1” are generated at the same probability, and the generated bit signal is mapped to 148 symbols after passing through channel coding and interleaving. The mapped symbols are modulated using Gaussian Minimum Shift Keying (GMSK) or eight Phase Shift Keying (8PSK) and then transmitted in a multi-frame or burst format through the wireless channel 110 from the transmitter 100.
The receiver 120 receives the signal transmitted from the transmitter 100 through the wireless channel 110.
GMSK, although being a nonlinear modulation scheme, may perform approximation into a linear-modulated signal. Thus, a signal sampled at intervals of kTS/NS from a signal received by the receiver 120 through a frequency-selective channel may be expressed as follows:
                              y          k                =                                            e                              j                ⁢                                                                  ⁢                kv                                      ⁢                                          ∑                                  i                  =                  0                                                                      N                    s                                    ⁡                                      (                                          L                      -                      1                                        )                                                              ⁢                                                          ⁢                                                x                                      k                    -                    i                                                  ⁢                                  e                                                            j                      ⁡                                              (                                                  k                          -                          i                                                )                                                              ⁢                                          θ                      /                                              N                        s                                                                                            ⁢                                  h                  i                                                              +                      n            k                                              [                  Equation          ⁢                                          ⁢          1                ]            
wherein k indicates a time index, and i indicates a running index for summation. xk indicates a transmitted symbol at time k, and nk indicates a term in which an additive complex interference and a background noise at the time k are summed. TS indicates a symbol time of a unit symbol and equals 48/13 μsec (≈3.69 μsec), and NS indicates an oversampling rate (the number of times of sampling per unit symbol, which may have, for example, a value of “4”). A function hk of a physical channel having a length of NS(L−1) is a result including effects of transmit filtering at the transmitter 100, receive filtering at the receiver 120, and the frequency-selective physical channel at the wireless channel 110. L indicates a length of a channel to be estimated and may have, for example, a value of 7. θ indicates a symbol rotation phase that varies with a modulation scheme, and may have a value of π/2 for the GMSK modulation scheme and a value of 3π/8 for the 8PSK modulation scheme. ν(:nu) indicates a carrier frequency offset phase that is normalized to 1/TS.
FIG. 2 is a view for describing a burst received by a receiver as the concept of sampling time to describe the concept of timing offset estimation in a GSM system.
Referring to FIG. 2, for example, one burst 200 may include a total of 156 symbols. The 156 symbols may sequentially include 4 guard symbols 202, 3 tail symbols 206, 58 first encrypted symbols 210, 26 training sequence symbols 214, 216, 218, 58 second encrypted symbols 212, 3 tail symbols 208, and 4 guard symbols 204. Selectively, the 26 training sequence symbols may include 6 front training sequence symbols 214, 16 middle training sequence symbols 216, and 4 back training sequence symbols 218.
At reception reference sampling time, the receiver stores, in a burst buffer, samples corresponding to a total of the 156 symbols (i.e., 156*NS samples) including the guard symbols 202 before four symbols from a right Downlink (DL) timing offset 201 (hereinafter, referred to as a “timing offset”). Herein, a timing offset indicates an offset from a start point of the received burst to a point at which a right DL signal is received.
A signal transmitted from the transmitter is received by the receiver after passing through a transmit filter of the transmitter, the wireless channel, and the receive filter of the receiver.
To perform frequency offset estimation and channel estimation, sampling instant optimization of the received signal is needed. Due to different communication environment, there is a reception time difference of the transmitted signal between the transmitter and the receiver or between the receiver and another receiver. Especially in the GSM system, timing offset estimation is important for correction of the time difference.
An optimal sampling instant has to be determined as an instant when maximum energy may be included in a channel estimation tap available for channel estimation. That is, the sampling instant has to be determined to use a channel estimation tap capable of including maximum energy available for channel estimation. The sampling instant is determined by a timing offset, and therefore, determination of an optimal timing offset is needed.